If for some \theta lying between 0^{\circ} and 90^{\circ}, \tan\theta=1, then what is the value of \sin^{2}\theta-2\sin\theta\cos\theta?

Explanation

Since \tan\theta = 1, \theta = 45^{\circ}. Thus, \sin 45^{\circ} = \cos 45^{\circ} = \frac{1}{\sqrt{2}}. The expression is (\frac{1}{\sqrt{2}})^2 - 2(\frac{1}{\sqrt{2}})(\frac{1}{\sqrt{2}}) = \frac{1}{2} - 1 = -\frac{1}{2}.

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